Q8: Team batting averages for Major League Baseball in a certain year are repres
ID: 3277608 • Letter: Q
Question
Q8:
Team batting averages for Major League Baseball in a certain year are represented below. Find the variance and standard deviation for each league. Compare the results.
National Leagues
Frequency
American League
Frequency
0.252 – 0.256
7
0.256 – 0.261
4
0.257 – 0.261
1
0.262 – 0.267
1
0.262 – 0.266
5
0.268 – 0.273
6
0.267 – 0.271
1
0.274 – 0.279
1
0.272 – 0.276
2
0.280 – 0.285
2
Q9:
Use Chebyshev’s theorem, solve these problems for a distribution with a mean of 57 and a standard deviation of 17. Round k and final answer to one decimal place.
At least what percentage of the values will fall between 23 and 91?
At least what percentage of the values will fall between 28 and 86?
National Leagues
Frequency
American League
Frequency
0.252 – 0.256
7
0.256 – 0.261
4
0.257 – 0.261
1
0.262 – 0.267
1
0.262 – 0.266
5
0.268 – 0.273
6
0.267 – 0.271
1
0.274 – 0.279
1
0.272 – 0.276
2
0.280 – 0.285
2
Explanation / Answer
Ans:
9) 23 and 91 are k=2 standard deviations aay from mean.
1-(1/4)=3/4 data is within 23 and 91
75% of the data lie within 23 and 91
28 and 86 are k=1.7 standard deviations away from the mean.
Hence,1-(1/1.7)2=1-0.346=0.654 i.e 65.4% of the data lie within 28 and 86
(Note:eat least 11/k2of the data lie within k standard deviations of the mean, that is, in the interval with with endpoints ±k for populations, where k is any positive whole number that is greater than 1.)
8)
National Leagues Frequency(f) m m*f (m-0.261)^2 0.252 – 0.256 7 0.254 1.778 0.000343 0.257 – 0.261 1 0.259 0.259 4E-06 0.262 – 0.266 5 0.264 1.32 4.5E-05 0.267 – 0.271 1 0.269 0.269 6.4E-05 0.272 – 0.276 2 0.274 0.548 0.000338 Total 16 4.174 0.000794 Mean= 0.260875 4.9625E-05 Variance 0.0070445 std devRelated Questions
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